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Vincent Toumazou and Jean-Francois Cretaux

Abstract

In the framework of physical field studies, EOF analysis allows the scientist to determine the modes that govern the variability of a phenomenon. The analysis requires the resolution of a linear algebra problem. This paper focuses on this part of the EOF analysis, the computation of some singular values, and the associated vectors of the data matrix D. After recalling some fundamentals of this type of problem, the authors compare the usually employed singular value decomposition strategy with a Lanczos eigensolver technique. The latter consists of computing some eigenvalues of a small symmetric matrix. The authors demonstrate its mathematical and numerical stability and discuss its main features. A comparison of the two strategies shows the advantages of the Lanczos technique. Finally, the approach is illustrated with an example based on the study of oceanographic datasets.

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Filipe Aires, Fabrice Papa, Catherine Prigent, Jean-François Crétaux, and Muriel Berge-Nguyen

Abstract

The objective in this work is to develop downscaling methodologies to obtain a long time record of inundation extent at high spatial resolution based on the existing low spatial resolution results of the Global Inundation Extent from Multi-Satellites (GIEMS) dataset. In semiarid regions, high-spatial-resolution a priori information can be provided by visible and infrared observations from the Moderate Resolution Imaging Spectroradiometer (MODIS). The study concentrates on the Inner Niger Delta where MODIS-derived inundation extent has been estimated at a 500-m resolution. The space–time variability is first analyzed using a principal component analysis (PCA). This is particularly effective to understand the inundation variability, interpolate in time, or fill in missing values. Two innovative methods are developed (linear regression and matrix inversion) both based on the PCA representation. These GIEMS downscaling techniques have been calibrated using the 500-m MODIS data. The downscaled fields show the expected space–time behaviors from MODIS. A 20-yr dataset of the inundation extent at 500 m is derived from this analysis for the Inner Niger Delta. The methods are very general and may be applied to many basins and to other variables than inundation, provided enough a priori high-spatial-resolution information is available. The derived high-spatial-resolution dataset will be used in the framework of the Surface Water Ocean Topography (SWOT) mission to develop and test the instrument simulator as well as to select the calibration validation sites (with high space–time inundation variability). In addition, once SWOT observations are available, the downscaled methodology will be calibrated on them in order to downscale the GIEMS datasets and to extend the SWOT benefits back in time to 1993.

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